The dynamic impact forces caused by wheel defects such as a flat have been of primary concern for freight trains operating at high speeds. A pitch plane model of a railway vehicle coupled with a comprehensive three-layer track system model is developed to study impact forces generated at the wheel-rail (W-R) interface in the presence of wheel flats. The W-R interaction is described by the non-linear Hertzian contact spring, while the rail is represented by a continuous Euler beam. The Rayleigh-Ritz method is used to solve the coupled partial and ordinary differential equations of the vehicle-track system. An idealized haversine wheel flat with the rounded corner is included in the W-R contact model. The W-R interface forces are evaluated under single or multiple flats on a single as well as multiple wheels. The forces transmitted to the bearings, pads, and the ballast are also evaluated under impacts due to single as well as multiple wheel flats. The results obtained through parametric analyses are discussed in view of a desirable design and operating condition to reduce the magnitude of impact loads. The results suggest that the rail mass, rail pad stiffness and damping, bending stiffness of rail, and ballast mass affect the W-R impact force considerably, apart from the flat size and vehicle speed. The influence of phase between the multiple flats on the resulting magnitudes of impact forces is also evaluated. The results suggest that the impact loads due to two flats are comparable with those due to a single flat when the spacing between the two flats exceeds 45. Furthermore, the magnitude of impact force due to a single wheel flat could be greater than that due to in-phase flats on both wheels, which can be attributed to the pitch dynamics of the bogie.